s11_mthsc208_hw01

s11_mthsc208_hw01 - MthSc 208, Spring 2011 (Differential...

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Unformatted text preview: MthSc 208, Spring 2011 (Differential Equations) Dr. Macauley HW 1 Due Friday January 21st, 2010 (1) Let P ( t ) be the net worth of an investment after t years, that is growing at a 5% rate. Suppose that after two years, the investment is worth $200. Write down an initial value problem (the differential equation & initial condition) for P , and sketch its solution. (2) Let T ( t ) be the temperature of a cup of water t minutes after being placed in a room where the ambient temperature is 72 . (a) Write down a differential equation that T satisfies. (b) Sketch the solution curve of the solution satisfying T (0) = 100. (c) Sketch the solution curve of the solution satisfying T (0) = 40. (d) Sketch the solution curve of the solution satisfying T (0) = 72. (3) Repeat the previous exercise, except let T ( t ) be the temperature of a sheet of metal (which cools down and heats up much quicker than water). Qualitatively, what is the difference between the solution curves in these two problems? Which value ofbetween the solution curves in these two problems?...
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This note was uploaded on 03/11/2012 for the course MTHSC 208 taught by Professor Staufeneger during the Spring '09 term at Clemson.

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